At the opening of Twitter’s East Coast headquarters on Thursday, Mayor Michael Bloomberg took the time to remember Jobs.

“In so many areas of the human experience, Steve had pushed the frontiers of what’s possible; and he took all of us along for a ride,” Bloomberg said. “This country and this world is a lot better because of it.”

“Steve’s legacy’s, a hundred years from now, and a hundred years after that; will be the feeling that life can be made better, that life can be more productive, that life can be more fun. That feeling; felt by each new generation; is really what changes the world.”

“He revolutionized animation. He put the computer in our pockets and, by virtue of that, made our lives entirely mobile. The iPhone that I carry and the iPad in front of me have both fundamentally changed how I communicate and how I access and store information and how I conduct business,” Bloomberg said.

A makeshift tribute has popped up in front of the Apple Store at 57th Street and Fifth Avenue. People have been leaving flowers, candles, notes and McIntosh apples.

“I wanted to say ‘Thank You’ to everything that Steve Jobs has done. He’s created so much of what I use in my life and what so many millions of people currently use and have been using. It’s just really awful that he had to die at such a young age,” said Cosmo Sharf.

“I think someone really, really important for all generations has passed away,” said Anna Mello.

One man told 1010 WINS’ Steve Sandberg that Jobs was a revolutionary. “For me, he’s just been a huge influence on my life. He’s inspired not only Apple people but competitors to push the limits of technology and make things happen.

“Edison, he helped open up new worlds, but Steve Jobs helped connect new worlds,” another man said.

Steven James of Bethlehem, Penn. wrote Jobs was an “American inventor that touched all of our lives in many ways.”

“This is a true tragedy,” wrote Maureen Farrelly Marsala.

“Thanks for all, Steve,” wrote New Yorker Rob Glenn.

Visitors to the Apple website are greeted today by a black and white photo of Jobs, and a brief statement.

“Apple has lost a visionary and creative genius, and the world has lost an amazing human being. Those of us who have been fortunate enough to know and work with Steve have lost a dear friend and an inspiring mentor. Steve leaves behind a company that only he could have built, and his spirit will forever be the foundation of Apple,” says the statement.

President Barack Obama also released a statement.

“Steve was among the greatest of American innovators – brave enough to think differently, bold enough to believe he could change the world, and talented enough to do it,” Obama said.

The flagship Apple store on Fifth Avenue. (credit: Anne Driscoll/CBS)

“For those of us lucky enough to get to work with Steve, it’s been an insanely great honor. I will miss Steve immensely,” Microsoft founder Bill Gates said.

Jobs knew long ago that personal computing would be more than a hobby, and would eventually become an essential part of our lives.

“It’s not going to happen at once. It’s just going to be very gradual and very human, and will seduce you into learning how to use it,” he said.

Jobs never lost that unique foresight. After co-founding Apple in 1976 at the age of 20 with his best friend Steve Wozniak in a garage, he set about becoming the consummate salesman, who ditched the suit and tie in favor of blue jeans and a black turtleneck, and earning the respect of even his competition.

Joshua Stone is a history teacher and on Thursday, he taught his high school students about persverance through Steve Jobs’ rollercoaster career.

“He’s a prime example of picking yourself back up even after you’ve fallen a few times and becoming one of the great innovators of our country,” Stone told CBS 2’s Cindy Hsu.

That message of perseverance has been passed down.

“It just teaches me, that when I have a failure or if something happens that I shouldn’t give up — that I should keep pulling through,” said Eleanor Bent.

His nontraditional, avant-garde approach was stitched into Apple.

“And I think creating great products is what people remember the most. And I think that’s what brings them something in their hearts and makes people happy,” Wozniak said.

Jobs stepped down from Apple’s CEO in August near the end of his battle with pancreatic cancer.